How to fix non-uniform shading after making object from curve by screw modifier?
about the non uniform shading in your pictures, it could also be that your starting curve was not properly aligned /centered on the screw axis, so the screw has repeated a tilt that was in you curve, hence the shading.

I roughly created this in a similar way, and I get no fuzzy shading:



without applying the modifier, you can convert this to 3d mesh using ALTC (the modifier will be removed, the effect is just like if it was applied) - I had to recalc the normals, after, anyway.

[edit] the "peak" you see is because I fastly drew a curve in this shape:



anyway another way is draw the bezier, convert it to mesh, and then screw - using "calc order" in the modifier seems to give better normals, to me.

anyway even with a better "curve" with straight angles like this



i get no "peaks" but the weird shading comes back. It seems due to the normals in that area



one way to fix this is to get less straiht angles there, either using a somewhat smoothed starting curve (as my first one) or after applying the modifier, adding some loops, on both sides:

in edit mode 
CRTLR2



before applying, scale on X



then on the circle
CRTL R



before applying, scale a bit toward the center


and now it seems much better



[edit2]
after seeing you video, I got why is different: since your starting curve is closed, screw modifier gives weird shading con the "front circle" face. Again, adding two loops near the inner and outer circle edges gives a much better look.



here the result, flat and smooth shaded: